Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
138 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×C9×M16 | C2 | semidirect |
| 3. C9×#681 | C2 | semidirect |
| 20. #3955 | C9 | direct (N × H) |
| 23. C9×M16 | D5 | semidirect |
| 35. C5×M16 | C2×C9 | semidirect |
| 36. #681 | C2×C9 | semidirect |
| 51. C5×C9 | #100 | semidirect |
| 83. M16 | C9×D5 | semidirect |
| 93. C9 | #3955 | direct (N × H) |
| 103. C5 | C9×#100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×D20 | 2 |
| C5×C9×M16 | 2 |
| C9×#681 | 2 |
| C3×#3955 | 3 |
| C9×#100 | 5 |